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Asked by Prashant DIGHE | 26 May, 2020, 05:19: PM

Expert Answer

A metallic rod of length 1 m is rigidly clamped at its midpoint.

V e l o c i t y space o f space p r o p a g a t i o n space o f space l o n g i t u d i n a l space w a v e s space equals space v space equals space square root of E over rho end root space equals space square root of fraction numerator 2 cross times 10 to the power of 11 over denominator 8000 end fraction end root space equals space 5 cross times 10 cubed space m divided by s I n space t h e space a b o v e space d i a g r a m comma space t h e r e space a r e space t w o space n o d e s space o n space e i t h e r space s i d e space o f space m i d p o i n t space a n d space m i d p o i n t space i s space n o d e space... left parenthesis a s space p e r space t h e space g i v e n space i n f o r m a t i o n right parenthesis L e n g t h space o f space r o d space equals space fraction numerator 5 lambda over denominator 2 end fraction equals space 1 space m space lambda equals 0.4 space m space f r e q u e n c y comma space nu space equals v over lambda space equals space fraction numerator 5000 over denominator 0.4 end fraction equals space 12500 space H z E q u a t i o n space o f space s tan d i n g space w a v e space i s space y space equals space open parentheses A space sin fraction numerator 2 pi over denominator lambda end fraction x space plus space B space cos space fraction numerator 2 pi over denominator lambda end fraction x close parentheses cos space 2 pi nu t space equals space open parentheses A space sin space 5 pi x space plus space B space cos space 5 pi x space close parentheses cos space 2 pi nu t space N o w comma space y space equals 0 space space a t space x space equals space 1 over 10 comma space 3 over 10 comma 5 over 10 comma space 7 over 10 comma 9 over 10 space m space T h u s comma space A space equals space 0 H e n c e comma space E q u a t i o n space o f space s tan d i n g space w a v e space i s space g i v e n space a s comma space y space equals space B space cos space 5 pi x space cos 2500 pi t space A s space t h e space a m p l i t u d e space a t space a n t i n o d e space equals space 2 cross times 10 to the power of negative 6 end exponent space m space y space equals space 2 cross times 10 to the power of negative 6 end exponent space open parentheses space cos space 5 pi x space cos 2500 pi t space close parentheses T h u s comma space y space equals space 1 cross times 10 to the power of negative 6 end exponent space space open parentheses space cos space 5 pi x plus space cos 2500 pi t space close parentheses space plus space 1 cross times 10 to the power of negative 6 end exponent space space open parentheses space cos space 5 pi x minus space cos 2500 pi t space close parentheses T h u s comma space t h e space c o m p o n e n t s space o f space t h e space w a v e s space a r e comma space y subscript 1 space equals space space 1 cross times 10 to the power of negative 6 end exponent space space open parentheses space cos space 5 pi x plus space cos 2500 pi t space close parentheses space y subscript 2 space equals space 1 cross times 10 to the power of negative 6 end exponent space space open parentheses space cos space 5 pi x minus space cos 2500 pi t space close parentheses space A t space a space p o i n t space 2 space c m space f r o m space m i d p o i n t space x space equals space left parenthesis 0.5 space plus-or-minus 0.02 space right parenthesis space m space T h u s comma e q u a t i o n space o f space m o t i o n space a t space t h i s space p o i n t space i s space g i v e n space a s comma space y space equals space space 2 cross times 10 to the power of negative 6 end exponent space open parentheses space cos space 5 pi x space cos 2500 pi t space close parentheses equals space space 2 cross times 10 to the power of negative 6 end exponent space open parentheses space cos space 5 pi space left parenthesis 0.5 space plus-or-minus 0.02 space right parenthesis space cos 2500 pi t space close parentheses space

Answered by Shiwani Sawant | 26 May, 2020, 07:51: PM

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